Question: Solve for $x$ : $ 3|x - 7| + 10 = 2|x - 7| + 2 $
Answer: Subtract $ {2|x - 7|} $ from both sides: $ \begin{eqnarray} 3|x - 7| + 10 &=& 2|x - 7| + 2 \\ \\ { - 2|x - 7|} && { - 2|x - 7|} \\ \\ 1|x - 7| + 10 &=& 2 \end{eqnarray} $ Subtract ${10}$ from both sides: $ \begin{eqnarray} 1|x - 7| + 10 &=& 2 \\ \\ { - 10} &=& { - 10} \\ \\ 1|x - 7| &=& -8 \end{eqnarray} $ Simplify: $ |x - 7| = -8$ The absolute value cannot be negative. Therefore, there is no solution.